Add 5 to Y, so the new values are 5, 8, 15, 6, 20.
Now compute the correlation between X and Y. Is the correlation smaller,
larger, or the same as before?

(d)

Multiply Y by 5, so the new values are 0, 15, 50, 5, 75.
Now compute the correlation between X and Y.
Is the correlation smaller,
larger, or the same as before?

(e)

Multiply Y by -1, so that the new values are 0, -3, -10, -1, -15.
Now compute the correlation between X and Y.
Is the correlation smaller, larger, or the same as before?

2.

The following data presents the per capita income of 20 European OECD countries
for 1960 and as well as the percentages of the labor force employed in
agriculture, industry, and services for each country.

Which among the three labor sectors provides the strongest
linear relationship with per capita income?

(b)

If majority of the labor force works in agriculture, would you
expect a higher per capita income?

(c)

Suppose PCINC (per capita income) is coded in thousands of
dollars instead, what happens to the correlation coefficients?

3.

Consider the first and second exam scores of 35 Stat 216 students:

Student

First

Second

Student

First

Second

1

21

22

19

25

22

2

23

23

20

13

19

3

16

19

21

17

22

4

23

19

22

23

18

5

23

24

23

11

21

6

17

21

24

17

14

7

12

18

25

18

11

8

15

16

26

13

16

9

20

20

27

18

11

10

8

10

28

16

15

11

22

24

29

21

17

12

22

22

30

15

9

13

23

22

31

16

22

14

18

19

32

22

16

15

22

23

33

18

16

16

20

20

34

21

13

17

20

20

35

19

24

18

20

20

(a)

Draw a scatterplot of the data. How are the two exam scores
related based on the plot? Would you say that this relationship
is strong?

(b)

Compute the correlation coefficient between the first
and second exam scores. Does this value support your judgment
in the previous question?

(c)

The Stat 216 director decided to curve the first exam scores by
giving away 5 points.

i.

Obtain a new scatterplot and compare this with the old plot.

ii.

What happens to the correlation coefficient? Explain this
behavior.

(d)

Fifth and eleventh students were found cheating
during the second exam. As a result, they were both
given zeros in that exam. What will happen now to the correlation
coefficient? Can you consider this new value reliable? Explain
why.